Tutorial Exercise

Find the derivative of the function.

$f(x)=\frac{8x}{(x^3-7{)}^2}$

Step $1$

Recall the Quotient Rule, which states that for a function of the form $f(x)=\frac{g(x)}{h(x)}$ the derivative is

$f^{\text{'}}(x)=\frac{h(x)g^{\text{'}}(x)-g(x)h^{\text{'}}(x)}{(h(x){)}^2}$

Thus, for the function $f(x)=\frac{8x}{(x^3-7{)}^2},$ we can let $g(x)=8x$ and $h(x)=$